{"id":771,"date":"2022-04-18T00:48:10","date_gmt":"2022-04-17T22:48:10","guid":{"rendered":"https:\/\/support.centreforelites.com\/?p=771"},"modified":"2022-04-18T00:48:22","modified_gmt":"2022-04-17T22:48:22","slug":"3-things-about-the-centre-of-mass","status":"publish","type":"post","link":"https:\/\/support.centreforelites.com\/ru\/3-things-about-the-centre-of-mass\/","title":{"rendered":"3 Things about the Centre of Mass"},"content":{"rendered":"<p class=\"wp-block-paragraph\"><strong><em>The centre of mass or mass centre is the&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">mean<\/a>&nbsp;location of all the&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">mass<\/a>&nbsp;in a system.&nbsp;<\/em><\/strong>In the case of a&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">rigid body<\/a>, the position of the centre of mass is fixed in relation to the body. In the case of a loose distribution of masses in&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">free space<\/a>, such as&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">shot<\/a>&nbsp;from a&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">shotgun<\/a>&nbsp;or the&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">planets<\/a>&nbsp;of the&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">solar system<\/a>, the position of the centre of mass is a point in&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">space<\/a>&nbsp;among them that may not correspond to the position of any individual mass.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"https:\/\/i0.wp.com\/educom360.com\/wp-content\/uploads\/2022\/03\/centreofmass2.gif?ssl=1\"><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/educom360.com\/wp-content\/uploads\/2022\/03\/centreofmass2.gif?ssl=1\" alt=\"The centre of mass\"\/><\/a><figcaption>The centre of mass<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">The term&nbsp;<strong>centre of mass<\/strong>&nbsp;is often used interchangeably with&nbsp;<a href=\"https:\/\/educom360.com\/glossary\/centre-of-gravity\/\"><strong>centre of gravity<\/strong><\/a>, but they are physically different concepts. They happen to coincide in a uniform gravitational field, but where gravity is not uniform,&nbsp;<strong>centre of gravity<\/strong>&nbsp;refers to&nbsp;<em>the mean location of the gravitational force&nbsp;<\/em>acting on a body.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The centre of mass of a body does not generally coincide with its geometric centre, and this property can be exploited. Engineers try to design a&nbsp;<em><a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">sports car<\/a>&#8216;s<\/em>&nbsp;centre of mass as low as possible to make the car&nbsp;<em><a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">handle<\/a><\/em>&nbsp;better. When&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">high jumpers<\/a>&nbsp;perform a &#8220;<strong><em><a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">Finsbury Flop<\/a><\/em><\/strong>&#8220;, they bend their body in such a way that it is possible for the jumper to clear the bar while his or her centre of mass does not.<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_88 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-6ab0571959f04\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-6ab0571959f04\"  aria-label=\"\u0422\u0443\u043c\u0431\u043b\u0435\u0440\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/support.centreforelites.com\/ru\/3-things-about-the-centre-of-mass\/#_CENTRE_OF_MASS_OF_A_REGULAR_OBJECT\" >&nbsp;CENTRE OF MASS OF A REGULAR OBJECT<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/support.centreforelites.com\/ru\/3-things-about-the-centre-of-mass\/#CENTRE_OF_MASS_OF_AN_ARBITRARY_2D_PHYSICAL_SHAPE\" >CENTRE OF MASS OF AN ARBITRARY 2D PHYSICAL SHAPE<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/support.centreforelites.com\/ru\/3-things-about-the-centre-of-mass\/#Centre_of_Mass_of_an_arbitrary_2D_physical_shape\" >Centre of Mass of an arbitrary 2D physical shape<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/support.centreforelites.com\/ru\/3-things-about-the-centre-of-mass\/#CENTRE_OF_MASS_OF_AN_L-SHAPED_OBJECT\" >CENTRE OF MASS OF AN L-SHAPED OBJECT<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"_CENTRE_OF_MASS_OF_A_REGULAR_OBJECT\"><\/span><strong>&nbsp;<\/strong><strong>CENTRE OF MASS OF A REGULAR OBJECT<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If an object has uniform&nbsp;<em><a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">density<\/a><\/em>&nbsp;then its centre of mass is the same as the&nbsp;<em><a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">centroid<\/a>&nbsp;<\/em>of its shape.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Examples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><em>The centre of mass of a ring is at the centre of the ring (in the air).<\/em><\/li><li><em>The centre of mass of a solid triangle lies on all three&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">medians<\/a>&nbsp;and therefore at the&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">centroid<\/a>, which is also the average of the three vertices.<\/em><\/li><li><em>The centre of mass of a rectangle is at the intersection of the two diagonals.<\/em><\/li><li><em>In a spherically symmetric body, the centre of mass is at the centre. This approximately applies to the&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">Earth<\/a>: the density varies considerably, but it mainly depends on depth and less on the&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">latitude<\/a>&nbsp;and&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">longitude<\/a>&nbsp;coordinates.<\/em><\/li><li><em>More generally, for any symmetry of a body, its centre of mass will be a fixed point of that symmetry.<\/em><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"CENTRE_OF_MASS_OF_AN_ARBITRARY_2D_PHYSICAL_SHAPE\"><\/span><strong>CENTRE OF MASS OF AN ARBITRARY 2D PHYSICAL SHAPE<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The&nbsp;<strong>Centre of Mass of an arbitrary 2D physical shape&nbsp;<\/strong>can be found using the following plumbline method as illustrated in the following table:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><a href=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEibou39AhukHICNIGSDSs5RpNXxNmHHhTbI_oK80FtgAZQVeDX-W1xv3jY7PVSvfdlok-8_2wpZ8FVrDquQ5yNORny90EOlaNI3xCJjBP9zBEij8qrd89EQ3FkmBnHwUh-VvlWqith32xcjFYryJTlub2CYzK7OvXRYGmBweSUp8qtqoE0JRGFGWa21=w164-h162\"><\/a><\/td><td><a href=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEiSleO1VFITTqHffp2N_9tw0BtF5Edo1sA7qN4fwK1IrjxpT93UIGpF_JJUp0XNPI3yStjcVTKZW0ugLDDoE00Le6DeZZ5ikedObf7PAmYmqRlsLus8o32mnqBuB5JGi5qebPAvcWLy5HkGry5IL-UacbRhV6U8zISC7IVDTkoRIdGM6SrOWDGesZjY=w162-h139\"><\/a><\/td><td><a href=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEjXVczFv6AVWqtQY7qcMbXgHzGeMtBBI523pGLM98x3S6POSRpjudeCZO2H-bkJTrp9qmem6fXubz9u8Bc5r5-01F7THw6wEAhWzGc2os-cNkJZPbQCgpeLkVNCHhJ0cE4MEH-bw0FvIrSLF-DF3CjTNCa2yS0KPc3_I1QCge2q7W4uwp4dTww_4tg6=w136-h161\"><\/a><\/td><\/tr><tr><td>Step 1:<strong>&nbsp;An arbitrary 2D shape.<\/strong><\/td><td><strong>Step 2:<\/strong>&nbsp;Suspend the shape from a location near an edge. Drop a&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">plumb line<\/a>&nbsp;and mark on the object.<\/td><td><strong>Step 3:<\/strong>&nbsp;Suspend the shape from another location not too close to the first. Drop a plumb line again and mark. The intersection of the two lines is the centre of mass.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Centre_of_Mass_of_an_arbitrary_2D_physical_shape\"><\/span><strong><em>Centre of Mass of an arbitrary 2D physical shape<\/em><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This method is useful when one wishes to find the&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">centroid<\/a>&nbsp;of a complex planar shape with unknown dimensions. It relies on finding the centre of mass of a thin body of homogenous&nbsp;<a href=\"https:\/\/www.blogger.com\/blog\/post\/edit\/3718099119877372482\/2581316266513676231#\">density<\/a>&nbsp;having the same shape as the complex planar shape.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"CENTRE_OF_MASS_OF_AN_L-SHAPED_OBJECT\"><\/span><strong>CENTRE OF MASS OF AN L-SHAPED OBJECT<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This is a method of determining the centre of mass of an L-shaped object.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEg6L7L2zK2zdgFaCPk7_7HTTkItky61KpQnzphx1SzxDtgrHZKQH2CclMVlKF8lhwx7zLxLSJXFf1PxH9AnZVbqz2W5tIIw7YrdJ3AIsSwqLZgdyNNUyZUDesULbibemuRTn7SdXLSyvTCvSiBIeTc9tt5L6aebz4RCk2paJVLKZTbatd6t3jRrWV1Q=w640-h106\"><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEg6L7L2zK2zdgFaCPk7_7HTTkItky61KpQnzphx1SzxDtgrHZKQH2CclMVlKF8lhwx7zLxLSJXFf1PxH9AnZVbqz2W5tIIw7YrdJ3AIsSwqLZgdyNNUyZUDesULbibemuRTn7SdXLSyvTCvSiBIeTc9tt5L6aebz4RCk2paJVLKZTbatd6t3jRrWV1Q=w640-h106\" alt=\"Centre of Mass of an L-shaped object\"\/><\/a><figcaption>Centre of Mass of an L-shaped object<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">1.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Divide the shape into two rectangles, as shown in fig 2. Find the centre of masses of these two rectangles by drawing the diagonals. Draw a line joining the centres of mass. The centre of mass of the shape must lie on this line AB.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li>Divide the shape into two other rectangles, as shown in fig 3. Find the centres of mass of these two rectangles by drawing the diagonals. Draw a line joining the centres of mass. The centre of mass of the L-shape must lie on this line CD.<\/li><li>As the centre of mass of the shape must lie along AB and also along CD, it is obvious that it is at the intersection of these two lines; at O. (The point O may or may not lie inside the L-shaped object.)<\/li><\/ol>","protected":false},"excerpt":{"rendered":"<p>The centre of mass or mass centre is the&nbsp;mean&nbsp;location of all the&nbsp;mass&nbsp;in a system.&nbsp;In the case of a&nbsp;rigid body, the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":183,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"wds_primary_category":0,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[48,58],"tags":[61],"class_list":["post-771","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog","category-integrated-science","tag-science-education"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"The centre of mass or mass centre is the mean location of all the mass in a system. 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